On the topological equivalence of the Arrow impossibility theorem and Amartya Sen's liberal paradox

The Impossibility of a Paretian Republican?

Philip Pettit (2001) has suggested that there are parallels between his republican account of freedom and Amartya Sen’s (1970) account of freedom as decisive preference. In this paper, I discuss these parallels from a social-choice-theoretic perspective. I sketch a formalization of republican freedom, and argue that republican freedom is formally very similar to freedom as defined in Sen’s “min...

The impossibility of a Paretian republican? Some comments on Pettit and Sen

Philip Pettit (2001) has suggested that there are parallels between his republican account of freedom and Amartya Sen’s (1970) account of freedom as decisive preference. In this paper, I discuss these parallels from a social-choice-theoretic perspective. I sketch a formalization of republican freedom, and argue that republican freedom is formally very similar to freedom as defined in Sen’s “min...

The Hex Game Theorem and the Arrow Impossibility Theorem: the Case of Weak Orders

The Arrow impossibility theorem when individual preferences are weak orders is equivalent to the HEX game theorem. Because Gale showed that the Brouwer fixed point theorem is equivalent to the HEX game theorem, this paper indirectly shows the equivalence of the Brouwer fixed point theorem and the Arrow impossibility theorem. Chichilnisky showed the equivalence of her impossibility theorem and t...

Arrow theorems in the fuzzy setting

Throughout this paper, our  main idea is to analyze the Arrovian approach in a fuzzy context, paying attention to different extensions of the classical Arrow's model arising in mathematical Social Choice to aggregate preferences that the agents define on a set of alternatives. There is a wide set of extensions. Some of them give rise to an impossibility theorem as in the Arrovian classical  mod...

The Impossibility of a Paretian Liberal: Reply